"Yes it's true, we lost another valuable figure this morning," a senior Haqqani official said.

The Haqqanis are "the Kennedys of the Taliban movement," according to one Western official, because of its wealth and strong ties are with local tribes.

The Haqqanis, based in Pakistan, are blamed for more than 2,000 deaths of U.S. soldiers in Afghanistan, NBC News reported.

The Pakistani Taliban is responsible for more than 40,000 civilian deaths and 5,000 soldiers' deaths during its insurgency against the Pakistan government.

"The Taliban militants did not allow even local residents to go and see what had happened," witness Amjad Hussain told NBC News. "They blocked nearby streets leading towards the madrassa."

Hussain said that dozens of the militants arrived after the strike, closing off the area. Residents said the drone fired four rockets into the madrasa in Pakistan's Waziristan tribal region at 5:40 a.m. local time, 7:40 p.m. Wednesday ET.

It is the first U.S. drone strike in Pakistan since the Nov. 1 strike against Pakistani Taliban chief Hakimullah Mehsud, which created a power struggle in the insurgency.

"Initially we thought that a suicide bomber had hit the madrasa but later we confirmed it was a drone attack,” a security official said.

"The Haqqani network has been fighting for 35 years,” Anatol Lieven of King's College London told NBC News. "Anyone who thinks these people can be deterred by death has not been paying attention. The idea that they might surrender is fatuous."